Question: Simplify the following expression: $\sqrt{112}+\sqrt{175}-\sqrt{7}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{112}+\sqrt{175}-\sqrt{7}$ $= \sqrt{16 \cdot 7}+\sqrt{25 \cdot 7}-\sqrt{7}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{7}+\sqrt{25} \cdot \sqrt{7}-\sqrt{7}$ $= 4\sqrt{7}+5\sqrt{7}-\sqrt{7}$ Finally, simplify by combining the terms. $= ( 4 + 5 - 1 )\sqrt{7} = 8\sqrt{7}$